"""abs(a)"""

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return Fraction(abs(a._numerator), a._denominator, _normalize=False)

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[502] Fix | Delete

def __trunc__(a):

[503] Fix | Delete

"""trunc(a)"""

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if a._numerator < 0:

[505] Fix | Delete

return -(-a._numerator // a._denominator)

[506] Fix | Delete

else:

[507] Fix | Delete

return a._numerator // a._denominator

[508] Fix | Delete

[509] Fix | Delete

def __floor__(a):

[510] Fix | Delete

"""Will be math.floor(a) in 3.0."""

[511] Fix | Delete

return a.numerator // a.denominator

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[513] Fix | Delete

def __ceil__(a):

[514] Fix | Delete

"""Will be math.ceil(a) in 3.0."""

[515] Fix | Delete

# The negations cleverly convince floordiv to return the ceiling.

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return -(-a.numerator // a.denominator)

[517] Fix | Delete

[518] Fix | Delete

def __round__(self, ndigits=None):

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"""Will be round(self, ndigits) in 3.0.

[520] Fix | Delete

[521] Fix | Delete

Rounds half toward even.

[522] Fix | Delete

"""

[523] Fix | Delete

if ndigits is None:

[524] Fix | Delete

floor, remainder = divmod(self.numerator, self.denominator)

[525] Fix | Delete

if remainder * 2 < self.denominator:

[526] Fix | Delete

return floor

[527] Fix | Delete

elif remainder * 2 > self.denominator:

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return floor + 1

[529] Fix | Delete

# Deal with the half case:

[530] Fix | Delete

elif floor % 2 == 0:

[531] Fix | Delete

return floor

[532] Fix | Delete

else:

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return floor + 1

[534] Fix | Delete

shift = 10**abs(ndigits)

[535] Fix | Delete

# See _operator_fallbacks.forward to check that the results of

[536] Fix | Delete

# these operations will always be Fraction and therefore have

[537] Fix | Delete

# round().

[538] Fix | Delete

if ndigits > 0:

[539] Fix | Delete

return Fraction(round(self * shift), shift)

[540] Fix | Delete

else:

[541] Fix | Delete

return Fraction(round(self / shift) * shift)

[542] Fix | Delete

[543] Fix | Delete

def __hash__(self):

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"""hash(self)"""

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# XXX since this method is expensive, consider caching the result

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[548] Fix | Delete

# In order to make sure that the hash of a Fraction agrees

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# with the hash of a numerically equal integer, float or

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# Decimal instance, we follow the rules for numeric hashes

[551] Fix | Delete

# outlined in the documentation. (See library docs, 'Built-in

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# Types').

[553] Fix | Delete

[554] Fix | Delete

# dinv is the inverse of self._denominator modulo the prime

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# _PyHASH_MODULUS, or 0 if self._denominator is divisible by

[556] Fix | Delete

# _PyHASH_MODULUS.

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dinv = pow(self._denominator, _PyHASH_MODULUS - 2, _PyHASH_MODULUS)

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if not dinv:

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hash_ = _PyHASH_INF

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else:

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hash_ = abs(self._numerator) * dinv % _PyHASH_MODULUS

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result = hash_ if self >= 0 else -hash_

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return -2 if result == -1 else result

[564] Fix | Delete

[565] Fix | Delete

def __eq__(a, b):

[566] Fix | Delete

"""a == b"""

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if type(b) is int:

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return a._numerator == b and a._denominator == 1

[569] Fix | Delete

if isinstance(b, numbers.Rational):

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return (a._numerator == b.numerator and

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a._denominator == b.denominator)

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if isinstance(b, numbers.Complex) and b.imag == 0:

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b = b.real

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if isinstance(b, float):

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if math.isnan(b) or math.isinf(b):

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# comparisons with an infinity or nan should behave in

[577] Fix | Delete

# the same way for any finite a, so treat a as zero.

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return 0.0 == b

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else:

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return a == a.from_float(b)

[581] Fix | Delete

else:

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# Since a doesn't know how to compare with b, let's give b

[583] Fix | Delete

# a chance to compare itself with a.

[584] Fix | Delete

return NotImplemented

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def _richcmp(self, other, op):

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"""Helper for comparison operators, for internal use only.

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Implement comparison between a Rational instance `self`, and

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either another Rational instance or a float `other`. If

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`other` is not a Rational instance or a float, return

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NotImplemented. `op` should be one of the six standard

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comparison operators.

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[595] Fix | Delete

"""

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# convert other to a Rational instance where reasonable.

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if isinstance(other, numbers.Rational):

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return op(self._numerator * other.denominator,

[599] Fix | Delete

self._denominator * other.numerator)

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if isinstance(other, float):

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if math.isnan(other) or math.isinf(other):

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return op(0.0, other)

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else:

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return op(self, self.from_float(other))

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else:

[606] Fix | Delete

return NotImplemented

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def __lt__(a, b):

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"""a < b"""

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return a._richcmp(b, operator.lt)

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def __gt__(a, b):

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"""a > b"""

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return a._richcmp(b, operator.gt)

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def __le__(a, b):

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"""a <= b"""

[618] Fix | Delete

return a._richcmp(b, operator.le)

[619] Fix | Delete

[620] Fix | Delete

def __ge__(a, b):

[621] Fix | Delete

"""a >= b"""

[622] Fix | Delete

return a._richcmp(b, operator.ge)

[623] Fix | Delete

[624] Fix | Delete

def __bool__(a):

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"""a != 0"""

[626] Fix | Delete

return a._numerator != 0

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[628] Fix | Delete

# support for pickling, copy, and deepcopy

[629] Fix | Delete

[630] Fix | Delete

def __reduce__(self):

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return (self.__class__, (str(self),))

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[633] Fix | Delete

def __copy__(self):

[634] Fix | Delete

if type(self) == Fraction:

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return self # I'm immutable; therefore I am my own clone

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return self.__class__(self._numerator, self._denominator)

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[638] Fix | Delete

def __deepcopy__(self, memo):

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if type(self) == Fraction:

[640] Fix | Delete

return self # My components are also immutable

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return self.__class__(self._numerator, self._denominator)

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[643] Fix | Delete